Friday, September 07, 2007

Flip rows, columns, not burgers

I heard a simple puzzle: starting with an all 0's nXn matrix, can you get any nXn target bit matrix using flip operations where each flip operation complements *each* element in a row or in a column. Trivially, this is not possible in general. Some of the other puzzles of this genre have operations where the sign of each row or column may be reversed, and the goal may be maximize the total sum of the numbers such as in Berlekamp's switching game (coding theory connection here). If anyone knows of novel puzzles of this genre, please let me know.

1 Comments:

elad verbin said...

There's always the lights-out problem: see here, here or here. (The last one of these contains the algebraic solution of lights-out. I saw a better and nicer one in HTML about a year ago, but I can't seem to find it just now).

And of course, there's "light-out"'s close-but-hard friend, the sorting-by-reversals-related "graph clicking" problem. Ask me about it over email, or see here (PPT presentation).